# Visibility in a ringworld atmosphere?

So I am proposing a ring-world of approximately 1600 km diameter. The ring spins for earth like gravity. The ring itself would be several kilometers thick with Earth like variations in elevation (i.e. mountains less than ~8 km above sea level, with ocean trenches of similar depth) The atmosphere would also be the same composition as Earth's. The ring would have Earthlike lighting levels.

The question: How far could you see in any direction?

I would think there would be a limit to how far you could see before the atmosphere would haze and limit your sight distance when looking towards the horizon (although there wouldn't be a horizon; maybe along the ring is a better term), but looking upward further past a certain point the haze should fade and you would be able to see the farther sections of the ring. Is this correct?

Could someone help me out with specifics; distances, angles, etc? How would this change with elevation? Does less dense air equal farther sight distances?

Thanks!

• Yes, thin air helps resolving objects that are far away, but I think on your world that wouldn't make much difference. – Renan Jun 22 '16 at 17:22
• Kind of off-topic, but how are you proposing to contain an atmosphere similar to Earth's along the inside surface of a ring? – Travis Christian Jun 22 '16 at 21:26
• I was planning on end wall structures to contain the atmosphere. The walls would need to be deeper than the atmosphere so 50-100km or more tall, kind of like the sides of a bucket. – Josh King Jun 23 '16 at 0:12

## 1 Answer

I did some googling, and the best answer to how far the atmosphere of Earth would let you see if it went on forever was in this post in Reddit:

The dominant effect should be the diffraction limit of your eye. You can resolve two objects separated by an angle theta equal to wavelength of light / diameter of telescope. For your eye, theta ~ 500 nm / 0.5 cm = 1e-4 radians. If you had a building H meters tall at a distance of D, then you could see tan(theta) ~ theta ~ H/D (the first part comes from the small angle approximation), or H = 1e-4 * D. So, at 10 km (1e4 m), you could resolve a 1 meter object. At 10,000 km, you could resolve a 1 km structure. By "resolve", in this case, it would be your ability to see the object against the surface of the ground.

Ten thousand kilometers is larger than your ring world by around an order of magnitude, so while haze would affect visibility just as it does on Earth, you would be able to see quite well in all directions.

Now, one thing to consider about your atmosphere. If it has the same composition and density as ours, and in a ringworld with the same average temperature and gravity as those from Earth, the stratosphere should be approximately 18-19 km deep. Let's round it to twenty. This calculator (in the "Area of circle segment by radius and height" part of the page) gives us a chord length of aroud 504.38 kilometers. That's the longest distance light can travel in your world without leaving the atmosphere. That's two orders of magnitude greater than the distance to the horizon on sea level on Earth. Your world, though smaller than Earth, would provide its inhabitants with quite a sight.

Edit: Just to make things clear (no pun intended), haze and refraction would have their maximum effect on objects around 500 kilometers away from the observer. Farther than that, haze and refraction are actually reduced. But you'll see the whole ring in all directions without much distortion.

• Basically, the ground would mostly look flat with a great arch from one end of the sky to the other; the haze/horizon would foster the illusion, one would think. – Seeds Jun 22 '16 at 20:59
• @Seeds nice point. The arching point would be pretty close, though... This ringworld has half roughly the diameter of our own Moon. – Renan Jun 22 '16 at 21:19
• Yeah, not like a halo, or Niven's ringworld. – Seeds Jun 22 '16 at 22:12